Solving constrained Horn clauses modulo algebraic data types and recursive functions

This work addresses the problem of verifying imperative programs that manipulate data structures, e.g., Rust programs. Data structures are usually modeled by Algebraic Types (ADTs) in verification conditions. Inductive invariants such often require recursively defined functions (RDFs) to represent abstractions structures. From logic perspective, this reduces solving Constrained Horn Clauses (CHCs) modulo both ADT and RDF. The underlying with RDFs is undecidable. Thus, even a candidate inductive invariant Similarly, IC3-based algorithms for CHCs lose their progress guarantee: they may not find counterexamples when program unsafe. We propose novel IC3-inspired algorithm Racer RDF (i.e., automatically synthesizing invariants, as opposed only them done deductive verification). ensures despite undecidability theory, guaranteed terminate counterexample unsafe It works general class over ADTs called catamorphisms. key idea catamorphisms CHCs, via relationification , RDFs, using . Encoding allows learning properties catamorphisms, well preserving unsatisfiabilty original use abstractions, whereas encoding unfolding recursive definition, relying on it solutions. Abstractions ensure theory remains decidable. implement our approach Z3 show practice.